You're trying to solve a puzzle that involves arranging squares of numbers according to their missing values. Each square has dimensions 4 × 4, containing all the numbers between 1 and 16 inclusively, except for one missing number represented by "?". All of these 4 × 4 squares are stored side-by-side within a larger matrix mat with dimensions 4 × (4 * n) (where n represents the number of square matrices).

Your task is to complete the following steps:

• For each 4 × 4 square, find the value of the missing element and replace the "?" with this value.
• Rearrange the squares inside the larger matrix by these missing values in ascending order. In the case of a tie (if two 4 × 4 matrices have the same missing value), place them in the relative order they were originally presented in the larger matrix mat.

Return the updated matrix mat as a result.

Example

• For

mat = [["1",  "2",  "3",  "4"],
       ["?",  "5",  "6",  "10"],
       ["13", "16", "12", "15"],
       ["9",  "7",  "8",  "14"]]

the output should be

sortByMissingNum(mat) = [["1",  "2",  "3",  "4"],
                         ["11", "5",  "6",  "10"],
                         ["13", "16", "12", "15"],
                         ["9",  "7",  "8",  "14"]]

The given matrix mat contains only one 4 × 4 square, so we just find the missing value in it (11), and replace the "?" with this value.

• For

mat = [["14", "3", "10", "4",  "16", "10", "?",  "2",  "?", "9",  "15", "11"],
       ["16", "7", "8",  "2",  "1",  "4",  "8",  "3",  "3", "16", "7",  "13"],
       ["?",  "9", "6",  "5",  "14", "12", "7",  "6",  "2", "10", "4",  "14"],
       ["15", "1", "13", "12", "9",  "15", "5",  "13", "1", "8",  "12", "6"]]

the output should be

sortByMissingNum(mat) = [["5", "9",  "15", "11", "14", "3",  "10", "4",  "16", "10", "11", "2"],
                         ["3", "16", "7",  "13", "16", "7",  "8",  "2",  "1",  "4",  "8",  "3"],
                         ["2", "10", "4",  "14", "11", "9",  "6",  "5",  "14", "12", "7",  "6"],
                         ["1", "8",  "12", "6",  "15", "1",  "13", "12", "9",  "15", "5", "13"]]

Input/Output

• [execution time limit] 3 seconds (java)

• [input] array.array.string mat

  A matrix of strings, where each element is equal to either "?" or a number from the inclusive range [1..16] in string form. It's guaranteed that the width of the given matrix is divisible by 4, and that each 4 × 4 square contains unique values.

  Guaranteed constraints:
  mat.length = 4,
  4 ≤ mat[i].length ≤ 500.

• [output] array.array.string

  Return the resulting matrix, after mutating it as described in the problem description.

[Java] Syntax Tips

// Prints help message to the console
// Returns a string
// 
// Globals declared here will cause a compilation error,
// declare variables inside the function instead!
String helloWorld(String name) {
    System.out.println("This prints to the console when you Run Tests");
    return "Hello, " + name;
}